   Chapter 10.1, Problem 90E

Chapter
Section
Textbook Problem

# Proof Prove that the graph of the equation A x 2 + C y 2 + D x + E y + F = 0 is one of the following (except in degenerate cases).Conic Condition(a) Circle A = C (b) Parabola A = 0   o r   C = 0   ( but   not   both ) (c) Ellipse A C > 0 (d) Hyperbola A C < 0

(a)

To determine

To Prove: The graph of the equation Ax2+Cy2+Dx+Ey+F=0 is a Circle when A = C.

Explanation

Proof:

With the help of GeoGebra Graphing calculator draw the graph as below.

Step 1: Click on the Input Button.

Step 2: Press on the “+” button which is near the input button; make sure that it’s on “Expression” Form.

Step 3: Write the provided expression in the Input column, in this case being x2+y2

(b)

To determine

To Prove:

The graph of the equation Ax2+Cy2+Dx+Ey+F=0 is a Parabola when A =0 or C = 0.

(c)

To determine

To Prove: The Graph of the equation Ax2+Cy2+Dx+Ey+F=0 is an Ellipse when AC > 0.

(d)

To determine

To Prove: The Graph of the equation Ax2+Cy2+Dx+Ey+F=0 is a Hyperbola when AC < 0.

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